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In this work we present 3-algebraic constructions and representations forthree-dimensional N = 5 supersymmetric Chern-Simons theories, and show how theyrelate to theories with additional supersymmetries. The N = 5 structureconstants give theories with Sp(2N) \times SO(M) gauge symmetry, as well asmore exotic symmetries known from gauged supergravity. We find explicit liftsfrom N = 6 to 8, and N = 5 to 6 and 8, for appropriate gauge groups.

Three-Algebras in N = 5, 6 Superconformal Chern-Simons Theories: Representations and Relations